New York state students' math and reading scores on standardized exams plunged this year, which federal and state officials said could be a harbinger of results in dozens of states moving to tougher tests tied to new curriculum standards.

Overall, 31% of New York state students in third through eighth grade were proficient in math and reading on state exams this year, down from 65% in math and 55% in English in 2012 on different tests, according to several people who had seen the results that will be officially released...